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Finite dimensional approximations for Nica-Pimsner algebrasApr 22 2019We give necessary and sufficient conditions for nuclearity of Cuntz-Nica-Pimsner algebras for a variety of quasi-lattice ordered groups. First we deal with the free abelian lattice case. We use this as a stepping stone to tackle product systems over quasi-lattices ... More

Invariant measures for Cantor dynamical systemsApr 21 2019This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a homeomorphism has either a unique ergodic invariant measure or finitely ... More

Distribution of Small Values of Bohr Almost Periodic Functions with Bounded SpectrumApr 19 2019If $f$ is a nonzero Bohr almost periodic function on $\mathbb R$ with a bounded spectrum we prove there exist $C_f > 0$ and integer $n > 0$ such that for every $u > 0$ the mean measure of the set $\{\, x \, : \, |f(x)| < u \, \}$ is less than $C_f\, u^{1/n}.$ ... More

Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groupsApr 19 2019We prove that the Grand Lebesgue Space, builded on a unimodular locally compact topological group, forms a Banach algebra relative to the convolution.

High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graphApr 19 2019The Kubo-Martin-Schwinger condition is a widely studied fundamental property in quantum statistical mechanics which characterises the thermal equilibrium states of quantum systems. In the seventies, G. Gallavotti and E. Verboven, proposed an analogue ... More

Optimal approximation order of piecewise constants on convex partitionsApr 18 2019We prove that the error of the best nonlinear $L_p$-approximation by piecewise constants on convex partitions is $\mathcal{O}\big(N^{-\frac{2}{d+1}}\big)$, where $N$ the number of cells, for all functions in the Sobolev space $W^2_q(\Omega)$ on a cube ... More

Rellich, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applicationsApr 18 2019In this paper we obtain weighted higher order Rellich, weighted Gagliardo-Nirenberg, Caffarelli-Kohn-Nirenberg inequalities and the uncertainty principle for Dunkl operators. Moreover, we introduce an extension of the classical Caffarelli-Kohn-Nirenberg ... More

Positivity of $2\times 2$ block matrices of operatorsApr 18 2019We review some of the significant generalizations and applications of the celebrated Douglas theorem on the equivalence of factorization, range inclusion, and majorization of operators. We then apply it to find a characterization of the positivity of ... More

Some results on almost L-weakly and almost M-weakly compact operatorsApr 17 2019In this paper, we present some necessary and sufficient conditions for semi-compact operators being almost L-weakly compact (resp. almost M-weakly compact) and conversely. Mainly, we prove that every semi-compact operator from a nonzero Banach space $X$ ... More

Extensions of the vector-valued Hausdorff-Young inequalitiesApr 16 2019In this paper we study the vector-valued analogues of several inequalities for the Fourier transform. In particular, we consider the inequalities of Hausdorff--Young, Hardy--Littlewood, Paley, Pitt, Bochkarev and Zygmund. The Pitt inequalities include ... More

Discrete Iterated Modified Projection Method for Urysohn Integral Equations with Non-smooth KernelsApr 16 2019In the present paper we consider a discrete version of the iterated modified projection method for solving a Urysohn integral equation with a kernel of the type of Green's function. For $r \geq 0,$ a space of piecewise polynomials of degree $\leq r $ ... More

Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysisApr 16 2019We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the $\overline \partial$-derivative near the real domain. We work in a general ... More

Sylvester equations and polynomial separation of spectraApr 16 2019Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of $p(A)$ and $p(B)$ ... More

On the Spectrum of Self--Adjoint Lévy GeneratorsApr 16 2019We investigate the spectrum of the generator of a self-adjoint transition semigroup of a (symmetric) L\'{e}vy process taking values in $d$--dimensional space.

Inverse of $\mathcal{U}$-frequently hypercyclic operatorsApr 16 2019We show that there exists an invertible $\mathcal{U}$-frequently hypercyclic operator on $\ell^p(\mathbb{N})$ ($1\le p <\infty$) whose the inverse is not $\mathcal{U}$-frequently hypercyclic.

$d$--$σ$--stability in random metric spaces and its applicationsApr 16 2019In 2010, the first author of this paper introduced the notion of $\sigma$--stability for a nonempty subset of an $L^0(\mathcal{F},K)$--module in [T.X. Guo, Relations between some basic results derived from two kinds of topologies for a random locally ... More

On $d$--$σ$--stability in random metric spaces and its applicationsApr 16 2019Apr 18 2019In 2010, the first author of this paper introduced the notion of $\sigma$--stability for a nonempty subset of an $L^0(\mathcal{F},K)$--module in [T.X. Guo, Relations between some basic results derived from two kinds of topologies for a random locally ... More

Embeddings of uniform Roe algebrasApr 15 2019In this paper, we study embeddings of uniform Roe algebras. Generally speaking, given metric spaces $X$ and $Y$, we are interested in which large scale geometric properties are stable under embedding of the uniform Roe algebra of $X$ into the uniform ... More

Isomorphism in WaveletsApr 15 2019Two scaling functions $\varphi_A$ and $\varphi_B$ for Parseval frame wavelets are algebraically isomorphic, $\varphi_A \simeq \varphi_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be $d\times d$ ... More

Structure and $K$-theory of $\ell^p$ uniform Roe algebrasApr 15 2019In this paper, we characterize when the $\ell^p$ uniform Roe algebra of a metric space with bounded geometry is (stably) finite and when it is properly infinite in standard form for $p\in [1,\infty)$. Moreover, we show that the $\ell^p$ uniform Roe algebra ... More

Compactification, and beyond, of composition operators on Hardy spaces by weightsApr 15 2019We study when multiplication by a weight can turn a non-compact composition operator on H 2 into a compact operator, and when it can be in Schatten classes. The q-summing case in H p is considered. We also study when this multiplication can turn a compact ... More

Hölderian convergence of fractional extended nabla operator to fractional derivativeApr 15 2019In this paper, we construct the fractional extended nabla operator as fractional power of linear spline of backward difference operator. Then we prove the strong convergence of this operator to fractional derivative in a H\"older space setting. Finally ... More

II$_1$ factors with exotic central sequence algebrasApr 15 2019We provide a class of separable II$_1$ factors $M$ whose central sequence algebra is not the "tail" algebra associated to any decreasing sequence of von Neumann subalgebras of $M$. This settles a question of McDuff \cite{Mc69d}.

Approximate Carath{é}odory's theorem in uniformly smooth Banach spacesApr 14 2019We study the 'no-dimension' analogue of Carath{\'e}odory's theorem in Banach spaces. We prove such a result together with its colorful version for uniformly smooth Banach spaces. In particular, we find the asymptotically tight upper bound on the deviation ... More

Prime II$_1$ factors arising from actions of product groupsApr 14 2019We prove that any II$_1$ factor arising from a free ergodic probability measure preserving action $\Gamma\curvearrowright X$ of a product $\Gamma=\Gamma_1\times\dots\times\Gamma_n$ of icc hyperbolic, free product or wreath product groups is prime, provided ... More

Noncommutative Orlicz sequence spaces and some applicationsIApr 13 2019In this paper, the definition of noncommutative Orlicz sequence spaces is given, these spaces generalize the Schatten classes Sp(H). After some relations of trace and norm on this spaces have been researched, one give the criterion of reflexivity of these ... More

Interpolation of compact bilinear operatorsApr 13 2019We investigate the stability of compactness of bilinear operators acting on the product of interpolation of Banach spaces. We develop a general framework for such results and our method applies to abstract methods of interpolation in the senseof Aronszajn ... More

Graded $K$-Theory, Filtered $K$-theory and the classification of graph algebrasApr 13 2019We prove that an isomorphism of graded Grothendieck groups $K^{gr}_0$ of two Leavitt path algebras induces an isomorphism of their algebraic filtered $K$-theory and consequently an isomorphism of filtered $K$-theory of their associated graph $C^*$-algebras. ... More

Approximation in the mean by rational functionsApr 12 2019Apr 19 2019For $1\le t < \infty$, a compact subset $K\subset\mathbb C$, and a finite positive measure $\mu$ supported on $K$, $R^t(K, \mu)$ denotes the closure in $L^t(\mu)$ of rational functions with poles off $K$. Let $\text{abpe}(R^t(K, \mu))$ denote the set ... More

Approximation in the mean by rational functionsApr 12 2019For $1\le t < \infty$, a compact subset $K$ of the complex plane $\mathbb C$, and a finite positive Borel measure $\mu$ supported on $K$, $R^t(K, \mu)$ denotes the closure in $L^t(\mu)$ of the rational functions with poles off $K$. Let $\text{abpe}(R^t(K, ... More

On the linearity of order-isomorphismsApr 12 2019A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of its engaged ... More

Order boundedness of weighted composition operators on weighted Dirichlet spaces and derivative Hardy spacesApr 12 2019In this paper, we completely characterize the order boundedness of weighted composition operators between different weighted Dirichlet spaces and different derivative Hardy spaces.

Extreme points of the set of elements majorised by an integrable function: Resolution of a problem by LuxemburgApr 12 2019Let $f$ be an arbitrary integrable function on a finite measure space $(X,\Sigma, \nu)$. We characterise the extreme points of the set $\Omega (f)$ of all measurable functions on $(X,\Sigma, \nu)$ majorised by $f$, providing a complete answer to a problem ... More

The Lanczos Algorithm Under Few Iterations: Concentration and Location of the Ritz ValuesApr 12 2019We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$. Let $A$ be an $n \times n$ Hermitian matrix. We show that when run for few iterations, the output of the algorithm on $A$ is almost deterministic. For ... More

Some Convergence Theorems for Operator SequencesApr 11 2019Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and $\left\{ \frac{1}{n}\sum_{i=0}^{n-1}A^{i}TB^{i}% ... More

Weak and approximate curvatures of a measure: a varifold perspectiveApr 11 2019By revisiting the notion of generalized second fundamental form originally introduced by Hutchinson for a special class of integral varifolds, we define a weak curvature tensor that is particularly well-suited for being extended to general varifolds of ... More

Range convergence monotonicity for vector measures and range monotonicity of the massApr 11 2019We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the strict convergence ... More

Uniformly convex and smooth Banach spaces and Lp-boundedness properties of Littlewood-Paley and area functions associated with semigroupsApr 11 2019In this paper we obtain new characterizations of the uniformly convex and smooth Banach spaces. These characterizations are established by using Lp-boundedness properties of Littlewood-Paley functions and area integrals associated with heat semigroups ... More

On orthogonal systems, two-sided bases and regular subfactorsApr 11 2019We prove that a regular subfator of type $II_1$ with finite Jones index always admits a two-sided Pimsner-Popa basis. This is preceeded by a pragmatic revisit of Popa's notion of orthogonal systems.

Essential self-adjointness of perturbed quadharmonic operators on Riemannian manifolds with an application to the separation problemApr 11 2019We consider perturbed quadharmonic operators, $\Delta^4 + V$, acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential $V$ satisfying a bound from below by a non-positive function depending on the distance ... More

Tight Bounds for the Subspace Sketch Problem with ApplicationsApr 11 2019In the subspace sketch problem one is given an $n\times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in an arbitrary way to build a small space data structure $Q_p$, so that for any given $x \in \mathbb{R}^d$, with probability ... More

Density results for Sobolev, Besov and Triebel--Lizorkin spaces on rough setsApr 10 2019We investigate two density questions for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) for an open set $\Omega\subset\mathbb R^n$, $\mathcal{D}(\Omega)$ is dense ... More

Regularized divergences between covariance operators and Gaussian measures on Hilbert spacesApr 10 2019This work presents an infinite-dimensional generalization of the correspondence between the Kullback-Leibler and R\'enyi divergences between Gaussian measures on Euclidean space and the Alpha Log-Determinant divergences between symmetric, positive definite ... More

Generalized-lush spaces revisitedApr 10 2019We study geometric properties of GL-spaces. We demonstrate that every finite-dimensional GL-space is polyhedral; that in dimension 2 there are only two, up to isometry, GL-spaces, namely the space whose unit sphere is a square (like $\ell_\infty^2$ or ... More

On Matrix Rearrangement InequalitiesApr 10 2019Given two symmetric and positive semidefinite square matrices $A, B$, is it true that any matrix given as the product of $m$ copies of $A$ and $n$ copies of $B$ in a particular sequence must be dominated in the spectral norm by the ordered matrix product ... More

Operators Whose Conjugation Orbits Satisfy Polynomial Growth ConditionsApr 10 2019Let $A$ be a bounded linear operator on a complex Banach space $X.$ For a given $\alpha \geq 0,$ we consider the class $\mathcal{D}_{A}^{\alpha }\left( \mathbb{R} \right) $ of all bounded linear operators $T$ on $X$ for which there exists a constant $C_{T}>0$, ... More

Generating wandering subspaces for doubly commuting covariant representations of product systemsApr 10 2019We obtain Halmos-Richter type wandering subspace theorem for covariant representations over $C^*$-correspondences. We further explore the notion of Cauchy dual and obtain Shimorin type Wold decomposition for covariant representations over $C^*$-correspondences ... More

Characterizations of derivationsApr 10 2019The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations. In Chapter 2 ... More

The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spacesApr 09 2019We consider r-ramification ultradifferentiable classes, introduced by J. Schmets and M. Valdivia in order to study the surjectivity of the Borel map, and later on also exploited by the authors in the ultraholomorphic context. We characterize quasianalyticity ... More

A bridge bewteen U-frequent hypercyclicity and frequent hypercyclicityApr 09 2019Given $\mathcal{A}$ the family of weights $a=(a_n)_n$ decreasing to $0$ such that the series $\sum_{n=0}^{\infty} a_n$ diverges, we show that the supremum on $\mathcal{A}$ of lower weighted densities coincides with the unweighted upper density and that ... More

A bridge between U-frequent hypercyclicity and frequent hypercyclicityApr 09 2019Apr 11 2019Given $\mathcal{A}$ the family of weights $a=(a_n)_n$ decreasing to $0$ such that the series $\sum_{n=0}^{\infty} a_n$ diverges, we show that the supremum on $\mathcal{A}$ of lower weighted densities coincides with the unweighted upper density and that ... More

Approximation in $L^p(μ)$ with deep ReLU neural networksApr 09 2019We discuss the expressive power of neural networks which use the non-smooth ReLU activation function $\varrho(x) = \max\{0,x\}$ by analyzing the approximation theoretic properties of such networks. The existing results mainly fall into two categories: ... More

Generalized Drazin-meromorphic invertible operators and generalized Kato-meromorphic decompositionApr 09 2019A bounded linear operator $T$ on a Banach space $X$ is said to be generalized Drazin-meromorphic invertible if there exists a bounded linear operator $S$ acting on $X$ such that $TS=ST$, $STS=S$, $ TST-T$ is meromorphic. We shall say that $T$ admits a ... More

Martingale Optimal Transport DualityApr 09 2019We obtain a dual representation of the Kantorovich functional defined for functions on the Skorokhod space using quotient sets. Our representation takes the form of a Choquet capacity generated by martingale measures satisfying additional constraints ... More

Entropy numbers of finite dimensional mixed-norm balls and function space embeddings with small mixed smoothnessApr 09 2019We study the embedding $\text{id}: \ell_p^b(\ell_q^d) \to \ell_r^b(\ell_u^d)$ and prove matching bounds for the entropy numbers $e_k(\text{id})$ provided that $0<p<r\leq \infty$ and $0<q\leq u\leq \infty$. Based on this finding, we establish optimal dimension-free ... More

On distributional adjugate and derivative of the inverseApr 09 2019Let $\Omega\subset\er^3$ be a domain and let $f\in BV_{\loc}(\Omega,\er^3)$ be a homeomorphism such that its distributional adjugate $\Adj Df$ is a finite Radon measure. Very recently in \cite{HKL} it was shown that its inverse has bounded variation $f^{-1}\in ... More

A summability principle and applicationsApr 09 2019The main result of the present paper is a new Inclusion Theorem for summing operators, that encompasses several recent similar results as particular cases. As applications, we improve estimates of certain Hardy--Littlewood inequalities for multilinear ... More

Plans on measures and AM-modulusApr 09 2019For measuring families of curves, or, more generally, of measures, $M_p$-modulus is traditionally used. More recent studies use so-called plans on measures. In their fundamental paper [4], Ambrosio, Di Marino and Savar\'e proved that these two approaches ... More

On upper bounds for regularity indices related to approximation theoryApr 09 2019We study the interrelation between the limit $L_p(\Omega)$-Sobolev regularity $\overline{s}_p$ of (classes of) functions on bounded Lipschitz domains $\Omega\subseteq\mathbb{R}^d$, $d\geq 2$, and the limit regularity $\overline{\alpha}_p$ within the corresponding ... More

On Riemann Integration in Metrizable Vector SpacesApr 09 2019In classical analysis, Lebesgue first proved that $\mathbb{R}$ has the property that each Riemann integrable function from $[a,b]$ into $\mathbb{R}$ is continuous almost everywhere. This property is named as the Lebesgue property. Though the Lebesgue ... More

A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS $L^{2}$ spacesApr 09 2019We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as "the" Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral ... More

On complex symmetric block Toeplitz operatorsApr 09 2019In this paper, we study complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we give a characterization of complex symmetric block Toeplitz operators with the special conjugation on the vector-valued Hardy space $H_{{\mathbb ... More

Clark measures on the complex sphereApr 08 2019Let $B_d$ denote the unit ball of $\mathbb{C}^d$, $d\ge 1$. Given a holomorphic function $\varphi: B_d \to B_1$, we study the corresponding family $\sigma_\alpha[\varphi]$, $\alpha\in\partial B_1$, of Clark measures on the unit sphere $\partial B_d$. ... More

Arov--Krein entropy functionals and indefinite interpolation problemsApr 08 2019We generalize the notion of the Arov-Krein entropy functional for the case of generalized Nevanlinna functions and obtain a representation of these functionals on solutions of indefinite interpolation problems. The case of indefinite Caratheodory problem ... More

Ricci curvature of doubly warped products: weighted graphs v.s. weighted manifoldsApr 08 2019We set forth a definition of doubly warped products of weighted graphs that is -- up to inner products of gradients of functions -- consistent with the warped product in the Riemannian setting. We establish Ricci curvature-dimension bounds for such products ... More

Convex Sobolev inequalities related to unbalanced optimal transportApr 08 2019We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical mechanics and population dynamics. These equations can be viewed as gradient ... More

Boundary values of holomorphic semigroups and fractional integrationApr 08 2019The concept of boundary values of holomorphic semigroups in a general Banach space is studied. As an application, we consider the Riemann-Liouville semigroup of integration operator in the little H\"older spaces $\rm{lip}_0^\alpha[0,\, 1] , \, 0<\alpha<1$ ... More

Metric characterization of the sum of fractional Sobolev spacesApr 08 2019We introduce a non-linear criterion which allows us to determine when a function can be written as a sum of functions belonging to homogeneous fractional spaces: for $\ell \in \mathbb{N}^*$, $s_i\in (0, 1)$ and $p_i \in [1, +\infty)$, $u : \Omega \to ... More

Unilateral weighted shifts on $\ell^2$Apr 08 2019Given a unilateral shift $B_w$ (determined by a bounded sequence $w$), a sequence $x \in \ell^2$ is "hypercyclic" for $w$ iff the forward iterates of $x$ under $B_w$ are dense in $\ell^2$. We show that it is possible to make the set of $x \in \ell^2$ ... More

Kantorovich problems and conditional measures depending on a parameterApr 07 2019We study measurable dependence of measures on a parameter in the following two classical problems: constructing conditional measures and the Kantorovich optimal transportation. We obtain broad sufficient conditions for the existence of conditional probabilities ... More

Prescribing tangent hyperplanes to $C^{1,1}$ and $C^{1,ω}$ convex hypersurfaces in Hilbert and superreflexive Banach spacesApr 07 2019Let $X$ denote $\mathbb{R}^n$ or, more generally, a Hilbert space. Given an arbitrary subset $C$ of $X$ and a collection $\mathcal{H}$ of affine hyperplanes of $X$ such that every $H\in\mathcal{H}$ passes through some point $x_{H}\in C$, and $C=\{x_H ... More

$L^0$--convex compactness and random normal structure in $L^0(\mathcal{F},B)$Apr 07 2019Let $(B,\|\cdot\|)$ be a Banach space, $(\Omega,\mathcal{F},P)$ a probability space and $L^0(\mathcal{F},B)$ the set of equivalence classes of strong random elements (or strongly measurable functions) from $(\Omega,\mathcal{F},P)$ to $(B,\|\cdot\|)$. ... More

Tracial moment problems on hypercubesApr 07 2019In this paper we study the tracial moment problem on the hypercube $[-1,1]^n$. We propose the concept "sequential tracial $K$-moment problem" for sequences of scalar matrices and establish a sufficient condition for the solvability of the sequential tracial ... More

Tracial moment problems on hypercubesApr 07 2019Apr 09 2019In this paper we introduce the "tracial $K$-moment problem" and the "sequential matrix-valued $K$-moment problem" and show the equivalence of the solvability of these problems. Using a Haviland's theorem for matrix polynomials, we solve these $K$-moment ... More

The Zak transform and representations induced from characters of an abelian subgroupApr 06 2019We consider a variant of the Zak transform for a finite group $G$ with respect to a fixed abelian subgroup $H$, and demonstrate a relationship with representations of $G$ induced from characters of $H$. We also show how the Zak transform can be used to ... More

Low-Rank Approximability and Entropy Area Laws for PDEsApr 06 2019We show how local interactions in a partial differential equation (PDE) model lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the ... More

Low-Rank Approximability and Entropy Area Laws for PDEsApr 06 2019Apr 11 2019We show how local interactions in a partial differential equation (PDE) model lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the ... More

Local average sampling and reconstruction with fundamental splines of fractional orderApr 06 2019We analyse sampling and average sampling techniques for fractional spline subspaces of $L^{2}({\mathbb{R}}).$ Fractional B-splines $\beta_{\sigma}$ are extensions of Schoenberg's polynomial splines of integral order to real order $\sigma > -1$. We present ... More

An improvement on the relatively compactness criteriaApr 06 2019This paper is devoted to the study of the relatively compact sets in Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness criteria for function ... More

Simultaneous approximation in Lebesgue and Sobolev norms via eigenspacesApr 06 2019We show how to approximate functions defined on smooth bounded domains by elements of eigenspaces of linear operators (e.g. the Laplacian or the Stokes operator) in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue ... More

Riesz transforms for Dunkl transforms on $L^\infty\left(m_k\right)$ and Dunkl-type $BMO$ spaceApr 06 2019In this paper, we define Riesz transforms for Dunkl transform for $L^\infty\left(m_k\right)$ in a weak sense. Then we will define Dunkl-type $BMO$ space and prove the boundedness of Riesz transform from $L^\infty\left(m_k\right)$ to Dunkl-type $BMO$ space, ... More

Generalizing Lieb's Concavity Theorem via Operator InterpolationApr 05 2019We introduce the notion of $k$-trace and use interpolation of operators to prove the joint concavity of the function $(A,B)\mapsto\text{Tr}_k\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big]^\frac{1}{k}$, which generalizes Lieb's concavity ... More

(Non-)amenability of the Fourier algebra in the cb-multiplier normApr 05 2019For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{Mcb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that $A_{Mcb}(G)$ is not amenable if $G$ contains a ... More

(Non-)amenability of the Fourier algebra in the cb-multiplier normApr 05 2019Apr 18 2019For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{Mcb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that $A_{Mcb}(G)$ is not amenable if $G$ contains a ... More

Decompositions with atoms and molecules for variable exponent Triebel-Lizorkin-Morrey spacesApr 05 2019We continue the study of the variable exponent Morreyfied Triebel-Lizorkin spaces introduced in a previous paper. Here we give characterizations by means of atoms and molecules. We also show that in some cases the number of zero moments needed for molecules, ... More

Spectral analysis of matrix scaling and operator scalingApr 05 2019We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent algorithm also has ... More

Elliptic problems and holomorphic functions in Banach spacesApr 05 2019In the first part we show that a vector-valued almost separably valued function $f$ is holomorphic (harmonic) if and only if it is dominated by an $L^1_\mathrm{loc}$ function and there exists a separating set $W\subset X'$ such that $\langle f,x'\rangle$ ... More

Continuity of extensions of Lipschitz mapsApr 05 2019We establish the sharp rate of continuity of extensions of $\mathbb{R}^m$-valued $1$-Lipschitz maps from a subset $A$ of $\mathbb{R}^n$ to a $1$-Lipschitz maps on $\mathbb{R}^n$. We consider several cases when there exists an extension with preserved ... More

On generalized Hölder's inequality in weak Morrey SpacesApr 05 2019In this note we reprove generalized H\"{o}lder's inequality in weak Morrey spaces. In particular, we get sharper bounds than those in \cite{gunawan2}. The bounds are obtained through the relation of weak Morrey spaces and weak Lebesgue spaces.

Kato S-spectrum in the quaternionic settingApr 05 2019In a right quaternionic Hilbert space, for a bounded right linear operator, the Kato S-spectrum is introduced and studied to a certain extent. In particular, it is shown that the Kato S-spectrum is a non-empty compact subset of the S-spectrum and it contains ... More

A bridge between quaternionic and complex numerical rangesApr 04 2019We obtain a sufficient condition for the convexity of quaternionic numerical range for complex matrices in terms of its complex numerical range. It is also shown that the Bild coincides with complex numerical range for real matrices. From this result ... More

Controlled $g$-frames in Hilbert $C^*$-modulesApr 04 2019To improve the numerical efficiency of iterative algorithms for inverting the frame operator, the controlled frame was introduced, and has been given more importance. In this paper, we introduce the concept of controlled g-frames in Hilbert $C^{*}$-modules. ... More

Controlled $g$-frames in Hilbert $C^*$-modulesApr 04 2019Apr 12 2019To improve the numerical efficiency of iterative algorithms for inverting the frame operator, the controlled frame was introduced by Balazs et al. \cite{Balazs}, and has since been given more importance. In this paper, we introduce the concept of controlled ... More

Thick Families of Geodesics and DifferentiationApr 04 2019The differentiation theory of Lipschitz functions taking values in a Banach space with the Radon-Nikod\'ym property (RNP), originally developed by Cheeger-Kleiner, has proven to be a powerful tool to prove non-biLipschitz embeddability of metric spaces ... More

Sets of $p$-restriction and $p$-spectral synthesisApr 04 2019In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set $E$ in $\mathbb{R}^n$ to have the $p$-restriction property. We also extend the concept of spectral synthesis to $L^p(\mathbb{R}^n)$ ... More

Self-adjointness of perturbed bi-Laplacians on infinite graphsApr 03 2019We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily bounded. The result ... More

Norm Inequalities for Inner Product Type Integral TransformersApr 03 2019In this paper, we give a detailed survey on norm inequalities for inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral ... More

On The Development of Nonlinear Operator TheoryApr 03 2019The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can fall in some ... More

Sequences of bounds for the spectral radius of a positive operatorApr 03 2019In 1992, Szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix $A$, based on the geometric symmetrization of powers of $A$. In 1998, Ta\c{s}\c{c}i and Kirkland proved a companion result by giving a sequence of upper ... More

Subdiagonal algebras with the Beurling type invariant subspacesApr 03 2019Let $\mathfrak A$ be a maximal subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$. If every right invariant subspace of $\mathfrak A$ in the non-commutative Hardy space $H^2$ is of Beurling type, then we say $\mathfrak A$ to be ... More